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Q No 1
5
Carry One
Mark
ach
1. Which one of the following is NOT a decision taken during the aggregate
production planning stage?
A) Scheduling of machines
B) Amount of labour to be committed
C) Rate
at
which production should happen
D) Inventory to be carried forward
Answer: -
B)
2 A CNC vertical milling machine has to cut a straight slot of 10mm width and 2mm
depth by a cutter of 10mm diameter between points (0,0) and 100,100) on the
XY plane dimensions
in
mm). The feed rate used
for
milling is 50mm/min.
milling time for the slot in seconds) is
A)
120
B)
170
C) 180
D)
240
Answer: - A)
3.
A solid cylinder of diameter
100mm
and height 50mm is forged between two
frictionless flat dies to a height of 25mm. The percentage change
in
diameter is
A) 0
B)
2.07 C) 20.7
D)
41.4
Answer: - D)
Exp:- From incompressibility we
get
rrdi h
1
= t d ~ h
2
d2
= lx l
d
2
= 1 x ~ = 141.42
d
d
Percentage change in
diameter=
2
1
x100
=
41.42
d
4. The velocity triangles at the inlet and exit of the rotor of a turbo machine are
shown. V denotes the absolute velocity of the fluid, W denotes
the
relative
velocity of the fluid, and
U
denotes the blade velocity. Subscripts 1 and 2 refer to
inlet and outlet respectively. I f
V
2
=
W
1
and
V
1
= W
2
then the degree of reaction
is
A) 0
Answer: - C)
B) 1
C) 0.5
D) 0.25
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5.
W hich one of the
fol lowin
g
con
figurations
has the highest
f in effect
iveness?
A) Thin
clo
sely spaced fi
ns
B) Thlnr
w id ely spaced
fins
C)Thick widely
spaced fi n
s
D) Thlckr
closely spaced
fins
Answer
: - A )
6.
An idea I gas
of mas s m and
ternperature
T
1
undergoes
a reversible
isotherm a
process fro
m
a
n in i t ia l pr
essure P
1
to
a
final pressure
P
2
. The heat
loss dur ing th
e
process is
Q.
The entropy change D.S
of
the
ga s
is
A)
mR
in P
2
)
B) m n
C) mRin
P
2
)- g
D)
Zero
A n
sw er: -
B
)
7.
In the m e
chanism g ive
n below
if
the
angu Ia r ve
loc i ty
of
the e
ccentr ic circu
Ia
r
disc
is
1ra
d/sr the
angular v
elocity rad/s) of the
fo l lowe
r link f
or
the
instant
show n in
the
f ig u re is
A ) 0.0
5
Answ
er: -
B)
B)
0.1
A ll d im ension
s are in
mm
C) 5.0
D) 10.0
8.
A circular so
lid disc of
un i f
o r m th ickness
20mm r rad iu s
200mm
and
mass 20kgr is
used as
a flywheel . If
it ro tates
at 600rpmr the k
inetic energy
of
the
f lywhee
lr in
Jou
les is
A)
395
B) 790
C) 1580
D) 3160
A nswer: -
B )
1
Exp:
K.E.
of
flywheel
= : Iw
2
I _ mR
2
_ 20
x 0.2
2
_
0
4
k
2
- - 2-
- 2 -
g
m
_
27tN _ 2 X 7tX600 _
6
2 83
d
/
w
- . ra
s
60
60
K.E
=
. .
x o.4x
62.83
2
=
790J
2
9. A cantilever
beam
of le n gth L is s
ubjec ted
to
a
m
oment M
at
the
f ree end
. The
mom
ent of inert
ia
of th
e beam
cross sect io
n about the n
eutral axis is
I and the
Young mod
ulus is E. The
m agn i tude
of
the
maxim
um deflect ion is
A) ML
2
B) ML
2
C)
2M L
2
D ) 4ML
2
2EI
EI
EI
EI
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Answer: - (A
)
Exp:- E d
2
y = M
dx2
upon lntigra tio
nr
EI
= Mx + C
1
Once again integratingr weget
Mx
El y
= - - +
C
1
X
+
C
2
2
For cantilev er
beam
at
x =
1
dy
= 0 x
= 0
y
= 0
dx
From th
is we
g
et C
1
= C
1
Or
Henc
e
Mx2
.
d fl
t
ML
2
y
=
2
EI ; max
1mum
e
ec
1 n
Ymax
=
2
EI
10
For a
long slender
column
of
un
iform cross s
ectionr the ra
t io
of
crit ical
buckling
load for th e ca
se
w
ith both
end s cia m pe
d
to
the case w
ith both ends
hinged is
A) 1
B
)
2
C) 4
D)
8
Answer: -(
C )
41t
2
EI
E xp :- C rltica I
Buckling load
for column fix
ed at both en
ds =
L
C
ritical Bucking
load for a c olu
mn hinged a
t both lands
2
;
1
11 . Atx=O, the fu nction f (x )
=X
3
+ 1
has
(A) A m a
x imum va lue
(C) A sing
ular i ty
Answ
e r: - ( D )
(B) A
m in imum v alu
e
(D) A p
oint
of
inflec
tion
Ex
p:- The
function
f x)=
x
3
+1
has
a
poin
t of in
flection at x =
0 since in
the graph
sign of
the curvatur
e
i.e.
1
the co
ncavity) is cha
nged.
y
.
~ ~ ~ ~
X
0
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12. For the spherical surface, x
2
+ y
2
+ z
2
-1 the unit outward normal vector at the
point
1-, ._1,o)
is given by
(A) _ _j+ __ __ J (B) __ __i __ __ J
(C)
k (D) _ _j+ __ __ j + __ __ k
J2 J2 J2 J2 J3 J3 3
Answer: - A)
Exp: -Given
spherical surface
is
x
2
+
y
2
+
z
2
= 1 and point is
. k
,
0)
Normal vector outward to x
2
+ y
2
+ z
2
-1=
0
at ..k ,
0} s
1 .
1 .
Ok 1 .
1 .
..{21+
..{2]+
.
=
..{21+ ..{2]
1 . 1 .
-1 -1
Hence the outward unit normal vector =
~
+ ~ : ] = }z i +
5:
j
13. Match the following metal forming processes with their associated stresses in the
workpiece.
List I
p
Coining
Q
Wire Drawing
R Blanking
s Deep
drawing
(A) P-4, Q-1, R-2,
S-3
(C) P-1, Q-2, R-4,
S-3
Answer: - A)
1
2
3
4
List II
Tensile
Shear
Tensile and compressive
Compressive
(B) P-4, Q-1, R-3,
S-2
(D) P-1, Q-3, R-2,
S-4
14. In abrasive
jet
machining, as the distance between the nozzle tip
and
the work
surface increases, the material removal rate
A) Increases continuously
B) Decreases continuously
(C) Decreases, becomes stable and then increases
D) Increases, becomes stable and then decreases
Answer: - D)
~ 0 0 4 0
15.
In
an interchangeable assembly, shafts
of
size 25. ooo-
0
010
m m mate with holes
of
~ 0 0 3 0
size
5 . o o o ~ o . o z o
m m . The maximum interference in microns) in the assembly is
A) 40 B) 30 C)
2 D)10
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Answ
er: - C)
Maximum in
terference=
m aximum siz
e of sh
aft-
m
inim um size
of hole
= 25.040-2
5 .020
=201 lm
16. Du
ring normalizin
g process
of steel, the spe
cimen is heate
d
A) Between
the upper and
lower crit ical t
em perature a
nd cooled in s
ti l l air
B) Above
the upper critical
tempera ture a
nd cooled in
furnace
C) Above
the upper crit ica
l tem pera ture
and cooled in
sti l lai
r
D ) Betwee
n the upper a
nd lower cr i t ic
al tempera tur
e and cooled
in fu rnace
Answ
er: - C)
17
. Oil f lows
through a 2
00m m d iame
ter horizontal
cast Iron pip
e friction fa
ctor,
f=O. 0225)
of length 500
m . The vo lum
etric f low ra
te Is 0.
2m
3
s. The head l
oss
in m) du
e to friction
is assume
g=9.
81mls
2
A) 116.18
B)
0.116
C) 18.22
D) 23
2.3 6
Answer:
- A)
Exp:-
0.022
5x500x
0
2
2
fL V
2
rrx 0.2
H
= =
4
=116.18m
2gD
2x9.81x0
.4
18. For an opaque surface, the absorptivity a), t ransit iv i ty
( t)
and re f lect iv i ty p) are
relate
d by the equa
tion
A)
a
p
= 1;
B)
p a t =
0 C)
a
p
= 1
D)
u
p
= 0
Answ
er: - C)
19.
Steam en
ters an adiab
atic turbine o
pera t ing
at
st
eady state wi
th n enthalp
y o
f
3
251.0kJikg a
nd le
a
ves
s a saturated
m
ixture
a
t
15
kPa with qua
lity dryness
fraction) 0.9. The enthalpies of
the
saturate d liquid and
va
pour at 15kPa are
ht=225.94
kJ ikg and hg=
2598.3kJ ikg
respect i vely. T
he mass flow
rate of steam
is
1
0kg ls. Kinetic
and potentia
I energy chan
ges are neg ll
glble. The pow
er outpu t of
the tur
b ine in
MW
is
:
A)
6. 5
B) 8. 9
C) 9.1
D ) 27.0
An sw er: -
B)
.
Exp:- Po
wer = m,x h
1
- h
2
) = 10 x
3251- 225.
94 + 0. 9x 2598. 3
- 225.94)
= 890010
Is
= 8.9MW
20. The
following are
the data for tw
o crossed he
licalgears use
d
fo
r speed r
eduction:
Ge
ar I :Pitch circ
le d iameter in
th e plane
of rotation 80mm
and helix an
gle 300.
G
ear II: Pitch
circle d iamete
r in th
e
plan
e o
f
rotation
120mm and
helix angle
22.50.
f the input speed is
1440rpm
, the output spee
d in rpm Is
A )
1200
B)
9 C
) 87 5
D) 72
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Answer: - (B
)
Exp: - For
helical gears
V I
It
t
. d
1
cos
80 cos 30
N
2
e
o
c y ra 10
=
=
d
2
COS
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24. Consider the function f(x) = lxl in the interval -1 :o;; x :o;; 1.
At
the point x=O, f (x) is
(A) Continuous and differentiable
C) Continuous and non-differentiable
Answer: - (C)
(B) Non-continuous and differentiable
(D) Neither continuous nor differentiable
Exp:- Given function is f(x) =
lx
1
1
x
1
is continues at x = 0 but not differentiable
25. lim (
1
- x) is
X-+0
X
A)
1/4
Answer: - (B)
Exp:- It
x ~ O
B)
1/2
C) 1
x ~
2sin
2
1) sin
2
1)
1 1
It = 2 It = 2
X
= -
x
x
x
J
4 2
- x4
2
Q No 6
Carry
Two Marks Each
D) 2
26. Calculate the punch size in mm, for a circular blanking operation for which details
are given below:
Size
of
the blank 25mm
Thickness of the sheet
Radial clearance between punch and die
Die allowance
A)
24.83
Answer: - (A)
(B) 24.89
2mm
0.06mm
0.05mm
(C) 25.01 (D) 25.17
Exp:- Diameter
of
punch= Diameter of Blank- 2 x radial clearance- die allowance
= 25-2x0.06-0.05= 24.83 mm
27.
In
a single
pass
rolling process using 410mm diameter steel rollers, a strip of
width 140mm and thickness 8mm undergoes 10 reduction of thickness. The
angle of bite in radians is
A)
0.006 (B) 0.031 (C) 0.062 (D)0.600
Answer: - (C)
Exp:-
~ H
=
D(1-cosa)
~
0.1x8
COSet
1 =
D 410
Ia
3.571
a 5 7 x ~ radians
Ia = 0.062 radians
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28. In aDC
arc welding
operation, the
voltage-arc
length chara c
teristic was ob
tained
a
s Vare = 20 +5
1 where the ar
c length I was
varied betwe
en
Sm
m and
7mm. Here
Varc
denotes the
arc voltage
in Volts. The
arc cu
rr
e
n
tw
as varied fro
m 400A
to
S
ODA Assuming li
near power so
urce charac te
ristic, the op
en circuit vo lt
ag e and
s
hort circuit cu
rrent for thew
elding operati
on are:
A) 45
V, 450A
B) 7SV,
SS
OA
C)
95V, 950A
D) lSOV, l
SOOA
Answ
er: -
C)
Exp:
Varc
= 20 5
I =
Smm
, Var
m = 45 V
1= 7mm, varc:fl =55
v
where V
0
is op
en c ircuit volta
ge
and 1
5
is sho r
t c i rcu i t curre
nt)
v
45 =V
0
-
x
s
oo
s
v
5
5 = V
0
- g x 4
00
I s
Upon solving
1)
and
2)
w
e
get
V
=
95
volts
Is
= 950A
29. A la
rge tank w ith
a nozzle a tt a
ched contain
s three Im mis
cible
in
viscid
fluids
as
sh
ow n. Assu m
in g that th e
changes in
h
11
h
2
and
h
3
are neg l
ig i ble, the
in stantaneou s
d ischarge vel
ocity is:
.
--
- - . - - . - - .
__
_ r
D )
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Answe
r: - (A)
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E xp :- Ap
plying Bernou
lli 's equat ion, a
t exit we ge
t,
Pl v;
P
2 i
-
gzl =
- gz2
P3 2
P
3
2
We kn
ow that Z
1
=
Z
2
, V
1
=
0 P
2
= Patm
H
ence
it
reduce
to
pl
V
P
3 2
v 2 =
~
p3
But P
=
P1
ghl
+ P2
gh2
+
p3gh3
Upon subst i tu
t ing we g
et
v 2
=
2
gh 3 [1
+
plh
l +
p2h2J
p2h3 p3h3
30.
Water (c P
=
4.
18kJ kgK) at
8ooc enter
s a coun te r flo
w heat excha
nger with a
ma ss f low
ra te o
f
O.S
kg/s. Air cp =
1kJ/kg K ) e
ntersat
3ooc with a mass
flow
ra t eof 2.09kg/s
. I f the ef f
ectiveness
of the h e
a
t exch
ange r is 0.8,
the LMTD ( in
OC is
(A )40
(B)
20
(C) 10
(D)
5
Answer: -
(C)
Exp:-
E = ~ X ~
- th
e
miR ~
- tc )
31
0
.
8
= 4.18 x
0.5 x 80- t;,.
2.09 x 1
80-
30)
t ht =
40C
mhcp th,
-
t,.,
= mccp, (tc, - tc,)
O.S
x 4.18 x
40 =2.09x1
x tc ,- 30)
t
ct
=
70C
9
1
=
9
2
=
10
C : LMTD
=
1
0C
A so lid
s teel cube co
nstrained on
a II six face s is
heated so tha
t th e tern pe
rature
ri s
es uni formly
by.L\.T. I f t
he thermal coe
fficient o f th e
material is
a Young's
m
odu lu s is E
and the Poiss
on's ratio is v
, th etherm al
s
tr
ess develo
ped in the
be du e to
heating is
(A) _ a .L\.
T ) E
(1 - 2v)
(B) _ 2a
.L\.
T
)
E
1-
2 v )
(C )
_ a.L\.T) E
(1 - 2v)
a .L\.T ) E
(D
) - 3 (1 - 2v )www.examrace.com
Answer: - (A
)
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32. A so li
d circu Ia r sha
ft needs to be
designed to
t ransmIt a tor
que
of SO
Nm.
If
the
al
lowable shear
stress of the
material is 14
DMPa, assum
ing a factorof
safety
of
2, the min i
mum al lowabl
e design diameter
in mm is
(A) 8
(B) 1
6
(C) 24 (D)32
Answer: -
(B)
Exp
:- T
=
SON-
n; allowable=
140MPa
fo.s
=
2;
C
=allowab
le =70MP
a
sa fe f
T
We
know, Zp =tsafe
Z
p =
1td
3
~
d 3
= 16T
16
1t safe
d = 16
x SDx 10
3
7t
X7
d = 1S .
3 8 m m
'16mm
0 5
33. A for
ce
of 40D
N is
applied
to
the
brake drum
of O.Sm
d iam
eter in a ban
d brake
system as s
hown in th e
figure, where
the wrappin
g angle is
180o. f the
coeffic ie
n t
of
friction b
etween the dr
um and the b
and Is D. 2S,t
he braking tor
que
applie
d, in
Nm
is
(A) 1
.6
Ans
w e r: - ( B)
~ t i
-
-
4
oON
(B) S4.4
C
) 22. 1
(D) 1S .7
Exp
:- As the dru
m is rotat ing
in anti clockw
ise direction,
T
1
will be tight
side T2w
ill
be clac
k side.
T
l =
e..e
=
.2Sx
=
2.19
T2
T
2
= 182
.37S N
Bre a
king torque = (T
1
-
T
2
) r
=
S4.4 N - m
34.
A box conta
ins 4 red bal
ls and 6 black
balls. Three
balls are sele
cted random ly
from the
box one a
f te r anotherwitho
ut replac
ement. The p
robabil ity that
the
s
ele cted set con
tains one red
ball and two
black balls Is
(A
)
__ __
2
0
1
B)
12
C )
~
10
(D) . .
2
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Answer: -
D)
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Red
Bla ck
Exp : - G iv
en,
4 6
Th e s
election will be
R
BB
or
BBR
of BRB
Pro
babil i ty
of
sele
ct ing
RBB
=
x
6
~
10 9 8
Prob
abil i ty
of
se le
ct ing
BBR
=
5
~
10
9 8
Probabllity of selectin g
BRB =
~ x:x
P Re
d=1)
=sum of
a bo
ve thre
e
pro b
abi l i t ies=
0.5
35
2 d
2
y dy
Consid e
r
the differential
equati o
n x -
+
x
4 y
= with the bo u
ndary
dx
2
d
x
condit ions
of
y(O )
=
0
and y 1)
=
1.
The com plete solut ion
of
the d if fe rent ia l
equat ion is
(B)
s i n ~ )
Answer: -
(A)
Exp : -
2
d
2
y
d
y
X -
X
4y = 0
dx
2
dx
Cau
chy s
D.
E
Y = x2
dy d
2
y
- =
2x -=2
d x
dx
2
m
2
4=
o
m
2
=
4
m
=
2
y(O )
= 0
y
1)
=
:
The
required so lut i
on is C
1
x
2
+
C
2
x
2
+ C
2
x
2
Hence the a
nswer is x
2
.
3
6. The sys
te m
of
algebra
ic equat ions g
iven below ha
s
X +
2y
+ Z = 4
2X
+ Y +
2Z = 5
X - Y + Z = 1
(A) A un i
que so lut ion
of x=1
y=1
an
d z=
1
D
) e-x sin ( 1t;
(B) O n
ly the two so lu
t ions
of x=1
y=1
and
z
=1)
and
x=2r y=
1
and z=O)
(C) In fi
nite num
ber of
s
olut ions
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D)
N
o feasible so l
ut ion
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7/21/2019 GATE Mechanical Engineering 2012
12/22
An
swe r: - (C)
E xp :-
The g ivene
quat ions are
X + 2y +
Z =
4
- (1)
2x
+
y
+2z =
5 - (2)
X
+
y
+ Z =
1
-(3)
Eliminating n f rom (1)
2) ,
we
have
y
=
1
-(4)
Elim
inating x fo rm
2) 3),
we
ha v e
y =
1
-(5)
Lines
4)
an
d
5)
are co inc
ident
H
ence
the
g ive
n equat ion ha
s infinite so lu t
ions
37. The ho
mogeneous s
ta te
of
stress
for a meta I
part
undergoin g
plast ic defo r
mat ion
I
s
T
= [150 a l
0
0 -
10
W he
re the stress
co
mponent
va
lues are in
MPa. Using von
Mises yield c
riterion,
the value
of
e
s t imated she a
r yield stress,
in
MPa
is
(A )
9.50
(B) 1 6 .07
(
C) 28 .52
D
)49.41
A
n sw e r: - (B)
Exp : -
eq
= { u - 0
22
)
2
+ 11
-
22 )
2
+
6 [ c
ri2
+ +
}
We know
, cr
11
= 10, cr
22
= 20,
0 33 =
-
10; 0 12
= 5; 0
23
= 0 13
= 0
Oeq
=
27.839 M P
a
0
S hear
stress
at
yie ld
Cy
=
Jj =16.
07 MPa
38. D eta
i ls pertaining
to an orthogo
nal me
tal
cu tt
ing process ar
e g iven below
Chip th ickness ratio 0.4
Unreform ed
th ickness
R
ake angle
C
utting speed
Mean th
ickness
of
pri
ma ry shearzo
ne
0.6mm
+10
0
2.5m/s
25 microns
The shear
stra in rate
in s-
1
dur ing
the process
is
(A
) 0 .1781 x 10
5
(B)
0.7754
x
10
5
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C
) 1.0104 x 10
5
D) 4.397 x 10
5
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7/21/2019 GATE Mechanical Engineering 2012
13/22
A
nswe r: - C )
Exp:- r = 0.4
t
1
=
0.6mm
a
=
10
Vc =
2
.5m/s
tm = 25
L
m
rcosa
o
~ =
.
= 0 4 2 3 3
~
= 2 2
9
1 - rstn
a
.
V
co
sa
S hear stra1n
rate=
os
- a x t m
2.
5 x
cos1
0 =
1
.
010
4x
10
s
/S
co
s12.9 x 25 x 10
39 . In a
sing le pass d
r i l l ing opera t
ion, a through
hole of 15mm diam
eter
is
to
be
dr i l led in a st
eel p la te
of
50mm
thickness. D rill spindle speed is
500rpm,
feed is
0
.2mm/rev
and d
rill pointangle is
11so . Assumin
g
2mm
clear
ance
at
appro
ach
and e
x it,
the
t
otal drill time in se
conds is
A) 35
.1
B) 32 .4
C)
31 .2
D) 30.1
Answ er: - A )
E
xp:- T = Lh +A+
+C)
c
f
Lh = 5
0mm;A = = 2
m m ;C = D
o t ~ ) 7.5 x co t
59 )= 4 .5mm
2 2
N = 500
rpm; f = 0. 2m
m rev
Tc = 0.585min
or35.1
Seconds
40
.
Consider two infin
i te l y lo n
g
th in
concen
tr ic
tub
es
of circu lar
cros
s section as
shown in
the
fi gure.
If D
1
and
the
d
iameters
of
th
e
inner and
ou
ter tu
bes
resp
ec tively, then
the
vi e
w factor F
2 2
is g iven
by
A) ~
B
) Zero
C)
~
~ : )
Answer: - D)
A D
Exp
:-
F
22
= 1 - F
2 1
=
1 -
1
= 1 -
_
A D2
41.
An Incompr
essible fluid fl
ows over a f l
a t p late w
ith zero pressure
gradient. Th
e
bounda
ry layer th ick
ness is
1m
m
at a location
where the R
eyn olds number
is
10
00. I f the ve
locity of the
fluid a lone
is increased by
a
fact
or
of
4
, th en the
boundary Iay
e r th ickness
at th e sa me lo
cation, in
m m
wil l be
www.examrace.com
(A ) 4
B) 2
(C ) 0.5
(
D)0.25
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7/21/2019 GATE Mechanical Engineering 2012
14/22
Answer: - (C
)
E xp :- Bound
ary lay
er
th ic k
ness
o) a
-
1
R
8
a
V
:::> S
a
JV
I f
ve locity
of fluid is in c
reased by 4 t
imes then bou
ndary layer t
hickness redu
ces
by ha l
f
42
. A ro om
conta ins 35k
g
of
dr
y
a
ir
a n
d 0.5g
of
w
ater vapour. Th
e
total
pressu
re and
temperatu
re o
f
a
ir
in the room
are 100kPa
and25
oc
res
pectively.
Gi
ve
n th
at the
saturat io n
pressure
fo r water
at 25oc is 3.17kPa, th
e re la t ive
h
umidity of the ai
r
in the r
oom is
A)
67
(B)
55 C
) 83
D)
71
Answer: - D)
43
. A fi l let-w
e lded
joint
is
subjected
to t ransverse lo
ading F as sh
own in the fi g
ure.
Bot
h legs
of
th e
f i l lets are
o
f
10m m size an
d
the
weldl
ength is 30 m m
. f
the
al lowable
shear stress
of the
weld
is
94 MP
a, considerin g
the
min
imum throa t a rea
of
th e w
eld, the
maximum al lowab l
e t ransverse l
oad In
kN
Is
(
A ) 14 .44
Answ er
: - C)
E xp :- P
= 0. 707
sl ,;a llowa
ble
(B)
17.92
P
= 0.707 x 10 x 30 x
94 = 19937.4N
P
19.934kM
(C) 19 .93
(D )
22.16
4
4. A conce
ntrated mass
m isat tached
at the
cen tr e
of
a rod
of
l
eng th 2L ass
hown
In
th
e
f igure. The
rod is kep t i
n a horizon ta
l equi l ibr ium
posi t ion by a
spring
of
st i f fness
k
F
or ve ry sm all
ampl
itudeof vibrat ion, ne
gle cting
the
w
eigh ts
of
the
rod and s
pr ing, the und
amped na tu r
a I frequen cy
of th system is:
(A)
(B )
k
C)
(D )
f
L
L
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Answer: - D)
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7/21/2019 GATE Mechanical Engineering 2012
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45.
The state
of stress
at
a
point under p l
ane stress con
dit ion Is
O xx = 40MPa;
O YY = 100MPa a
nd xy = 40MPa
The rad
ius of the Moh
r s circle repr
esent ing the g
iven sta te
of
s
tress in MPa i
s
(A) 40
(B)
50
(C) 60
(D)
100
Answe
r: - (B )
Exp:- O x
v = 40 MPa; O'w
= 100 MPa,
xv = 40M P
a
Radius
of
M
ohr s circle =
xx
+
,.2 = ./3o
2
+
4o2 = 50 MPa
' -0
J
2
xy
46.
The Inverse
Laplace transfo
rm of t
he
fun
ct ion F (s) =
(
1
) is give
n by
S
S + 1
A) f ( t ) =
sint
B)
f t )=e-
ts int
C)
f t
) = e-t
D)
f t)=1-e-t
A
nswer: - D )
Ex - L
1
1 J- . _
_
p.
5
5+1)
-
5
5+1
L
1 (. .-
_
1_
=
1e-t
5
S+
1
47.
For the matrix
A =
~ l O N E of
the no
rmalized
eigenvectors
is g iv
en as
(A) [ l
Answer: - B)
1
5-A
.
Exp
:-
lA
A.II =
0 ::;>
1
(B)
~
C) [ ~ l
.J
10
1 = 0 ~
5 - 1 . ) 3 - A . )
= 3 = 0
3-A.
:
:;> A.
2
- 8/ ,
+
5
3 = 0 A.
2
-
SA
.+ 12 =
0 /, = 2,
A.
=
6
A -
21
x
X= 0
At, A. =2
~
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7/21/2019 GATE Mechanical Engineering 2012
16/22
Hence
the required v
ector
Is
[
~
o
mmon
Data Quest ions
48 . 4
9
Two ste
el truss m em
bers
AC
and
B
C
each h
aving cross
sectional area
of
100mm
2
are subj ect
ed
to a hor izonta l fo rce F as sho w n
in
the
figure. Al l the
j
o in ts are hin g
ed.
A
48
. The
maximum force
Fin
kN that
can
be applied
a
t
C such
that th
e
axial stres
s in
any
o
f the truss m e
mb e r s
DO
ES
NOT exceed 1
00MPa
Is
A
)
8.
17
(B) 11
.15 (C )
14 . 14
D
)22.30
An
s w er: - (B )
Exp
: - From La
me s theore m r
F FA
FB
Sin105 S
in120 S in13
5
> F
A=
0.8 9
6 SF; FB =
0.
732F
:.maximu
m
force is FA a n
d s t r e s s
= ~ = 1 M P a
Area
0
8965
F
= 100MPa
>
F
= 11154.48
N
or 11.1SKN
1 0 0
4 9.
f F = 1
kN
,
the
magn i tud e
of the
ver t ica
I react ion forc
e developed
at
the
point
B
In
KN is
A) 0.63
(B)
0.32
C)
1. 26
Answer : -
(A)
vertlcaI eact ion
at point
B is R
8
=F
cos 30 = 0.633 F
F = 1KN
:.R
=0.63
3KN
Common Data Ques
t ions 50
. 51
D
) 1.46
A refr igera to
r operates b
etween 120 k
Pa and 800
kPa in
an ideal v apour
compre
ssion cycl e
with R-134a a
s the refr ige
rant . The re f
r igerant en te r
s the
www.examrace.com
com pressor as saturated vapour and leaves the condenser as satura ted liquid.
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7/21/2019 GATE Mechanical Engineering 2012
17/22
The mass
f low ra te of t
h e refri
gerant is 0.2kgl
s. Propert ies fo r
R-134a are
as
fo ll o
ws:
Sa tu ra ted
R-134a
P
kPa
)
TOC
h
1
k
J
kg )
h
9
k
J
kg )
st
kJ
kg K)
s
9
kJ
kg
K)
1 2 0
-22. 32
22.5
237
80
0 31 .3 1
95 5
267 3
Superheate d R-134a
P
kPa )
TC
h k
J kg)
800
40
276.45
50. T
he power req
uired for th e c
ompressor in
kW is
A ) 5 94
Answ
e r: - C)
E xp :-
T
4
B) 1 83
C) 7.9
L
s
Power
required
for
c
ompressor
= mr h
2
- h
1
)
0 .09 3
0
.95
0354
0.918
s kJ
kg K
0
.95
D) 39. 5
=
0.2x
276.45 - 237)
=
7.9kW
51
. The rate
at which hea t
is ext racte d in
k is f rom th e
ref r igerated
space is
A) 28 .3
B) 42
9
C) 3
4 .4
D) 14 6
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Answer: - A)
Exp: -
Rateat which
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7/21/2019 GATE Mechanical Engineering 2012
18/22
heat is
extracted=mr h
1
- h
4
=
0.2 237 -95.5)
28.3 kW
Stat
ement for Linked Ans
wer Questio
ns: 5
53
For a part icu lar project, e ig ht act i v ities are to
e
carried out. Their relationships
w it
h
o
ther acti v it i
es and expect
ed durat ions a
re me
nt
ioned
in the tab le b
elow.
Act iv i ty
P ed ece s
sors Du
ration da ys)
A
-
3
B
a
4
c
a
5
D
a
4
E
b
2
F
d
9
c.e
6
H
f,g
2
52. T
he crit ical path
for the projec
t is
A)
a-b-e-g-h
B) a-c-g-h
Answer: - C
)
C) a-d - f- h
D) a-b
-c- f -h
Exp :-
4
Varies
pathare
A B E G
H -17 days
A C G H
- 16 days
A D F H
-18 days ;
:
A D F H is c
ritica l path
2
4
6
F
9
6
53
. f the dur
at ion of act iv i
ty f a lone is ch
anged f rom 9
to 10 days, th
en the
A) Crit ical
path remains
the same and
the to ta l dura
t ion to comp l
ete the project
ch a
nges to 19da
ys
B) Crit i
cal path and th
e to ta l durat i
o n to complet
e the project
remain the sa
me
C) Critlca
I path chang
es but the
tota durat ion to
com plete the
p roject rema
ins
th
e same
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D) Critica l path changes and th e total dura t ion
to
co mple te the p ro je c t changes
to 17days
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7/21/2019 GATE Mechanical Engineering 2012
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Answer: -
A )
Exp : - I
f
d
ura t ion
of activity F has ch
anged to
10 days, cri t ica l
path remains
the same
and proj
ect
d
urat ion wi l l in c
rease
to
1 9d
ays.
State
ment forLinked
Ans
wer
Ques
tions: 54
55
Ai r
e nte rs an ad iabatic nozz le at 300kPa,
SOOK
w ith a veloc it y of
1Dm
ls
I t
l
ea
ves
th
e
nozzle
at 100kPa w
ith a veloc i ty
o
f
18Dmls. T
h
e
in le t area is
80cm
2
The
specif ic he
a t
of
air Cp is
1008J ikg .
K
54. T
he
exit
te
mperature
of
the a
i r is
A) 5 1 6 K
B) 53 2K
A ns we r: - C)
E xp :- h
1
v/ 2
=
h
2
v
2
v 2
_v
2
2 2 t
=
h
t - hz
= P
Tt -
Tz)
55.
180
2
2
-
102
= 1008X S OD - T
2
)
T
2
=
4
8 4 K
The exi t area
of
the nozzle
in
cm
2
is
C ) 484K
A)
90.1
B)
56.3
C) 4 .
4
A
n sw er : - D )
E xp
:- From con ti
nu i ty equa tio n
we get,
Vl = P
2A2V2
P
P
PT V
-
1
x V
= -
2
- x AzV
= _ _
RTt
t 1 RT2
2 PzTt
Vz
A = 300 x 48
4
x
10 x 80=12 9c
m2
2
50 0
x
100 180
Q.
No 56 - 60
CarryOne M
ark Each
D
) 468K
D) 12 .9
56.
The cos t fu
nct ion
for
a
product in a
firm is given b
y Sq
2
, w here
q is the
amou
nt
of
productio
n. The f irm c
an sell
the
produc t
at
a market price
of
RsSO
per un it.
The
number
of units to be pr
oduced by t
he f i rm such
tha
t
the
profit is
ma
x imized is
A) 5
Answer: A )
E xp :-
P
=
SOq -
Sq
2
B) 10
C)15
D) 25
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dp
d
2
p
dq =
SO
-
1Oq dq
2
0
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7/21/2019 GATE Mechanical Engineering 2012
20/22
: p Is m ximum
at
50
10
q 0 o
r, q 5
Else
check w it
h options
57. Ch
oose the m
ost appropria
te a l ternat ive
from the o
ptions given
below to
complete the
following se n
tence:
Suresh s dog is the one was hurt
in
the stampede.
(
A)
th t
(B) which
(C)
who
(D) whom
Answer: (A
)
58. Choos
e
the
gramma
tical ly
INC
ORRECT
senten
ce:
(A) The
y gave us the
money bac
k less the se
rvice charges
of
Three Hu
ndred
r
upees.
(B ) This country s expenditure is not less than
th t
of
Ban gladesh.
(C) Th
e commit tee
in i t ia l ly asked
for
a fundin g
of
Fifty Lak
h rupees, bu
t la ter
s
ett led fo
r
a
lesser sum.
(D
) This country
s expenditu re
on education
a I reforms Is
very less
Answer: (D
)
5
9. Which o
ne
o
f the fo l
lowing option
s is the close
st In meaning
to
the word
given
bel
ow?
M
it igate
(A) Dim
inish
A
nswer: (A)
(B) Divulge
(C) Ded
icate (D
) Denote
60.
Choose th
e most appr
opr iate ltern
tive from
the options gi
v
en
below
to
comple
te
the
follow in
g sentence:
Despite se
veral
the m
ission succeed
ed in i ts atte
mpt to resolve
the
co nfl let.
(A ) ttem
pts
Answer: (B )
(B) setbacks
C) m e
etings
(D) delegation
s
Q No
6
6 Carry Tw
o Ma
rks
E
ach
61.
Wanted Tem
porary, Part-
t ime persons
for
th
e post of
Field Inter
viewer to condu
ct
personal interv iews
to
collect and collate economic data. Requirements: High
Sc
hool-pass, must
be ava
ilable for D
ay, Evening
and Saturd
ay work.
Transportatio
n paid, expens
es reimbursed
.
W
hich one of t
he fo l lowing is
the
best in fe
rence from th
e above adver
t isement?
(
A) Gender-d is
cr iminatory
(B )
Xenophobic
(C) N
ot designed t
o
rna
ke the po
st attract ive
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(D ) No t gender-d is cr iminatory
Answer: (C)
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7/21/2019 GATE Mechanical Engineering 2012
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E xp:- G ender
Is not m entio
ned in the ad
ver t isementan
d (B) clearly
eliminated
62
. Given the
sequence of
termsr AD CG
FK JP, the ne
xt term is
(A)
OV
B)
OW
(C)
PV
(D)
PW
Answ
er: (A)
Exp:-
+2 +3
+4
+5
AD
I CG
I
FK
I JP
I v
. .
. . . . _ _ ~
~
-
+3
4 +5 Y
63.
Which of th e
following asse
rtions are CO R
RECl?
P: Adding 7 to
each entry in
a list adds7
to
the meanof
the list
Q:
Adding7
to
each
entry
in
a
l ist
adds7
to
the standard deviation of the list
R:
Doubling each
entry in a
list
doublesth
e mean of the
l ist
5: Doubling each
entry in a
I st
leaves the
standard devi
ation of the
I
s t
unchanged
(A) P, Q
B) Q, R
(C
) P, R
(D) Rr S
Answer
:
C)
Exp:- P
and R always
holds
true
Else
conside r
a sample se t
{1,
1 1
4} an
d check acco
rdingly
64 . An
automobilep
lant contracte d
to buy shock
absorbers fro
m two supplie
rs X andY.
X supplies
60
andY
su
pplies 40 of
the shock abs
orbers. All sho
ck absorbers a
re
subjec
ted to a qualit
y test. The one
s t hat pass the
quality testare
considered
reliable
O
f
X s
shock ab
sorbers, 96 a
re reliable. O f
Y s
shock abs
orbers, 72 a
re reliable.
Th
e probabil ity t
hat a randomly
chosen shock
absorber, whi
ch is found to
be rel ia
b
ler
Is
made byY
is
A)
0.288 B
) 0
.334 C )
0.667
(D) 0 .7
20
Answ
er:
B)
Exp:-
Supply
X
60
Reliable
96
Overa II
0. 576
: P(x ) =
0
288
=0.3
34
0.57
6 0 .288
y
40
72
0
.288
65. A
politicalparty
orders
an
arc
h
for
the entr
ance
to
the gr
ound
In
which
the annual
c
onvention isb
eing held. The
profileof the
arch follows t
he equation y
=
2x-
0.1x
2
w
here y is the
height of the
arch in meter
s . The ma xi m
um possibleh
eight
of
the
arch Is
(A) 8 m ete
rs (B )10
meters
(C) 12 mete
rs (D) 14
meters
Answ
er: (B)
Exp:-
y = 2x - 0.1x
2
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y
2 0.2x
x
-
7/21/2019 GATE Mechanical Engineering 2012
22/22
< 0 : ma
ximises
at 20
.2x
= 0
x
1
: y = 2 1
0 =1
0m
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